| 三阶非线性方程三点线性边值问题解的存在性与惟一性 |
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| 引用本文： | 杜媛芳,王国灿.三阶非线性方程三点线性边值问题解的存在性与惟一性[J].纺织高校基础科学学报,2009,22(1). |
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| 作者姓名： | 杜媛芳 王国灿 |
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| 作者单位： | 大连交通大学,理学院,辽宁,大连,116028 |
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| 摘 要： | 利用微分不等式技巧研究一类三阶非线性微分方程的三点线性边值问题.以二阶边值问题的已知结果为基础,建立了Volterra型积分微分非线性边值问题的解的存在性,再利用反证法获得了解的惟一性.同时,构造适当的上下解,得到了三阶非线性微分方程的三点线性边值问题的解的存在性与惟一性.结果表明,这种技巧为其他边值问题的研究提出了崭新的思路.
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| 关 键 词： | 三阶非线性方程 三点线性边值问题 存在性与惟一性 微分不等式 |
Existence and uniqueness of solutions for linear three-point boundary value problem for third-order nonlinear equation |
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| DU Yuan-fang,WANG Guo-can.Existence and uniqueness of solutions for linear three-point boundary value problem for third-order nonlinear equation[J].Basic Sciences Journal of Textile Universities,2009,22(1). |
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| Authors: | DU Yuan-fang WANG Guo-can |
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| Affiliation: | School of Math. & Phys.;Dalian Jiaotong University;Dalian;Liaoning 116028;China |
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| Abstract: | A class of linear three-point boundary value problems of third order nonlinear differential equation was studied by means of differential inequality theories.Based on the given results of second order boundary value problem, the existence of solutions of nonlinear boundary value problem of Volterra type integro-differential nonlinear equation was established. The uniquess of solution was obtained by applying disproof method.The suit upper and lower solution were constructed, and existence and unique of solu... |
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| Keywords: | third order differential equation three-point linear boundary value problem existence and uniqueness differential inequality |
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